Secondary school eighth grade students' conceptual images and operational understandings of the square root concept

The purpose of this research is to determine the concept images and operational understanding of the eighth grade secondary school students about the concept of square root. This research was sustained with a total of 12 students studying at the eighth grade level of a public school in the 2021-2022 academic year. The model of the research was designed as a case study, one of the qualitative research designs. The 12 middle school eighth grade students selected for the sample were determined using the disproportionate stratified sampling technique, which is one of the random sampling types. In the research, the data were obtained through the interviews made with the Test for Determining the Operational Understanding of the Concept of Square Root and the Semi-Structured Interview Form about the Concept of Square Root, which were applied to the students. The qualitative data obtained from the interviews were analyzed via descriptive analysis method to determine the concept images and operational understanding of the eighth grade students about the concept of square root. According to the findings obtained as a result of the research, middle school eighth grade students answered by using concept images while defining the concept of square root; In concept images, it was seen that they associated the square root concept with exponential expressions. In addition, it was seen that the eighth grade students of secondary school used the formal definitions of the concept of square root within the framework of operational understanding.